Related papers: On spectral flow for operator algebras
We give a functional analytical proof of the equality between the Maslov index of a semi-Riemannian geodesic and the spectral flow of the path of self-adjoint Fredholm operators obtained from the index form. This fact, together with recent…
We show that the (graded) spectral flow of a family of Toeplitz operators on a complete Riemannian manifold is equal to the index of a certain Callias-type operator. When the dimension of the manifold is even this leads to a cohomological…
Nondissipative force acting on a vortex in Fermi superfluids and superconductors is calculated from the spectral flow of fermion zero modes in the vortex core. The spectral flow effect casts a new light on the problem of mutual friction in…
In the classical operator theory, there are several versions of spectra, related to special classes of operators (Fredholm, semi-Fredholm, upper/lower semi-Fredholm,etc.). We generalize these notions for adjointable operators on Hilbert…
The spectral renormalization method is a powerful mathematical tool that is prominently used in spectral theory in the context of low-energy quantum field theory and its original introduction in [5, 6] constituted a milestone in the field.…
We prove in full generality a formula that relates the spectral flow of a continuous path of quadratic forms of Fredholm type with the spectral flow of the restrictions of the forms to a fixed closed finite codimensional subspace. We then…
In this article we study generalised Dirac-Schr\"odinger operators in arbitrary signatures (with or without gradings), providing a general KK-theoretic framework for the study of index pairings and spectral flow. We provide a general…
The spectral flow in the supersymmetric {\it t-J} model with $1/r^2$ interaction is studied by analyzing the exact spectrum with twisted boundary conditions. The spectral flows for the charge and spin sectors are shown to nicely fit in with…
We use spectral flow to present a new proof of Levinson's theorem for Schr\"{o}dinger operators on $\mathbb{R}^n$ with smooth compactly supported potential. Our proof is valid in all dimensions and in the presence of resonances. The…
A stable homology theory is defined for completely distributive CSL algebras in terms of the point-neighbourhood homology of the partially ordered set of meet-irreducible elements of the invariant projection lattice. This specialises to the…
The Vafa-Witten equations (with or without a mass term) constitute a non-linear, first order system of differential equations on a given oriented, compact, Riemannian 4-manifold. Because these are the variational equations of a functional,…
We build a combinatorial invariant, called the spectral monodromy from the spectrum of a non-selfadjoint h -pseudodifferential operator with two degrees of freedom in the semi-classical limit. We treat small non-selfadjoint perturbation of…
The paper pursues three objectives. Firstly, we provide an expanded version of spectral analysis of self-adjoint Toeplitz operators, initially built by M. Rosenblum in the 1960's. We offer some improvements to Rosenblum's approach: for…
We derive a decomposition formula for the spectral flow of a 1-parameter family of self-adjoint Dirac operators on an odd-dimensional manifold $M$ split along a hypersurface $\Sigma$ ($M=X\cup_{\Sigma} Y$). No transversality or stretching…
For a piecewise linear version of the periodic map with anomalous diffusion, the evolution of statistical averages of a class of observables with respect to piecewise constant initial densities is investigated and generalized eigenfunctions…
We consider R and NS spectral flow sectors of type IIB superstring theory on AdS(3)xS(3)xT(4) in the context of the AdS(3)/CFT(2) correspondence. We present a derivation of the vertex operators creating spectral flow images of chiral…
We present a fairly general construction of unbounded representatives for the interior Kasparov product. As a main tool we develop a theory of C^1-connections on operator * modules; we do not require any smoothness assumptions; our…
Based on our previous studies of the BRST cohomology of the critical N=2 strings, we construct the loop measure and make explicit the role of the spectral flow at arbitrary genus and Chern class, in a holomorphic field basis. The spectral…
Motivated by Fredholm theory, we develop a framework to establish the convergence of spectral methods for operator equations $\mathcal L u = f$. The framework posits the existence of a left-Fredholm regulator for $\mathcal L$ and the…
Naively, the analytic index of a family of self-adjoint Fredholm operators ought to be (an equivalence class of) the family of the kernels of these operators. The present paper is devoted to a rigorous version of this idea based on ideas of…